Full Idea
To be object for a subject and to be representation is to be one and the same thing. All representations are objects for a subject, all objects for a subject are representations.
Gist of Idea
Object for a subject and representation are the same thing
Source
Arthur Schopenhauer (Fourfold Root of Princ of Sufficient Reason [1813], §16 p.41-2), quoted by Peter B. Lewis - Schopenhauer 3
Book Reference
Lewis, Peter B.: 'Schopenhauer' [Reaktion Books 2012], p.73
A Reaction
This is pure idealism in early Schopenhauer, derived from Kant. Are being 'an object for a subject' and being an object 'in itself' two different things? Compare Idea 21914, written later. I think Nietzsche's 'perspective' representations helps here.
Related Idea
Idea 21914 We can deduce experience from self-consciousness, without the thing-in-itself [Fichte]